Each year, tropical cyclones (also referred to as hurricanes, typhoons and tropical storms) cause severe damage in various parts of the world. The occurrence of such weather events is difficult, if not impossible, to predict over the long term. Even the path, or track, of an existing storm can be difficult to predict over a period of hours or days.
Nevertheless, insurance companies and other entities need to develop ways of assessing the risks associated with such weather events, and factoring that knowledge into the pricing of insurance products and the magnitudes and frequencies of damages to expect over time. Information is available for use in this regard in the form of historical data on storms which have occurred through the years. Approximately 80 such storms occur worldwide each year. Data are collected on many of these storms, including positional data for the storm path or “track,” wind speeds, barometric pressures, and other factors. Such storms are best documented in the North Atlantic (i.e., the portion of the Atlantic Ocean north of the equator), where reliable data for more than 100 years of activity are available. Approximately 10 storms occur in the North Atlantic region on an annual basis. Historical data are also available for cyclones occurring in the Northwest Pacific, where approximately 26 storms occur each year. Suitable data for these Pacific storms are available only for the last approximately 50 years. Less data are available for storms in other regions.
Using all available historical data, information relating to a few hundred storms are available for review by researchers and scientists. Such information is useful in assessing risks associated with storm damages in the subject areas. However, given the unpredictable nature of storm behavior, and the number of factors influencing such behaviors, the available data set of historical storms is relatively small from a probabilistic viewpoint. Given that this data set will grow by only a relatively few storms per year, a problem exists with regard to performing statistical analysis relating to the possibility of a storm occurring at a particular location.
One manner in which this problem can be addressed is by generation of simulated or “alternative” storms, and using data from such “storms” to expand the data set available from historical records. This approach can result in the availability of thousands, or even tens or hundreds of thousands, of additional storms from which to create data sets large enough to perform reliable statistical analyses. The subject invention is directed to various embodiments involving uses of computer methods for generating such expanded probabilistic data sets.
One embodiment of the invention comprises a computer method for generating a probabilistic data set relating to a weather event, such as a tropical cyclone, or hurricane, typhoon, or tropical storm. This embodiment of the method includes the steps of inputting data representative of an historical track of a weather event and generating data representative of a plurality of alternative tracks based on the historical track. The data points representative of the alternative tracks are generated from respective points along the historical track by a dependent sampling process. In certain embodiments, the dependent sampling process is a directed random walk process.
In one embodiment, the step of generating data representative of alternative tracks based on the historical track comprises the steps of generating a series of random tuples (xr,yr) for a historical point (x,y) of the historical track, calculating a sum of random deviations (x′,y′) of the random tuples along the historical track, and adding the sum of random deviations (x′,y′) to the historical point (x,y) of the historical track to produce alternative points along the alternative tracks.
The data representative of the historical track(s) include a plurality of points representative of geographical positions along the historical track(s). The generated data representative of a plurality of alternative tracks includes a plurality of alternative points representative of geographical positions along the alternative tracks. In one embodiment, at least some of the plurality of alternative tracks associated with a particular historical track have starting points that differ from a starting point of the historical track upon which the alternative tracks are based. The data representative of the historical track may comprise longitude and latitude data to define a location of each of a plurality of points.
In certain embodiments of the method, the step of inputting data representative of an historical track includes the step of inputting at least one of: longitude and latitude of a plurality of points representative of the historical track; an azimuth angle for at least some of the points along the historical track; celerity for at least some of the points along the historical track; a rate of change of azimuth angle for at least some of the points along the historical track; and a rate of change of celerity for at least some of the points along the historical track. Alternatively, the latter values (azimuth, celerity, and rates of change of azimuth and celerity) may be calculated from longitude and latitude data recorded at periodic time intervals.
Some embodiments of the subject method further comprise the step of selecting a subset of the data representative of the alternative tracks for use in the probabilistic data set. In these or other embodiments, the step of generating data representative of alternative tracks includes the step of limiting a variance of the alternative points from a respective historical point in accordance with one or more physical laws.
In certain embodiments of the subject method, the step of inputting data representative of a track of an historical weather event includes inputting data representative of an intensity of the event. The data representative of intensity may comprise atmospheric pressure data associated with at least some of the plurality of points along the historical track. The atmospheric pressure data defines an historical pressure profile of the historical track. The atmospheric pressure data may include an absolute pressure and a derivative of (or change in) absolute pressure with respect to time. In certain embodiments, the atmospheric pressure data includes one or more pressure distributions. In some embodiments of the subject method, the step of inputting data includes inputting data representative of a plurality of historical tracks, and the step of establishing a grid over a geographical area of interest including at least a portion of the plurality of tracks. These embodiments may further comprise the step of establishing a pressure climatology for selected cells in the grid, based upon the atmospheric pressure data associated with at least some of the plurality of points along the historical tracks located within the selected grid cells. The pressure climatology for the selected cells may be a pressure distribution function. The pressure climatology for a selected cell in the grid may be established from the atmospheric data associated with the selected cell and/or the atmospheric pressure data associated with one or more cells adjacent the selected cell (i.e., one or more neighboring cell). In certain embodiments, the pressure climatology for a selected cell is established from a weighted averaging of pressure data associated with the selected cell and pressure data associated with one or more neighboring cell.
In certain embodiments, each cell in the grid is assigned a land/sea value. In these embodiments, pressure data associated with an adjacent cell is used to establish the pressure climatology of the selected cell only if the adjacent and the selected cell have the same land/sea value.
Certain embodiments of the subject method comprise the additional step of generating one or more alternative pressure profiles for one or more of the historical tracks using the pressure climatology for the selected cells in the grid. In addition, one or more pressure profiles may be generated for one or more of the alternative tracks. One or more alternative pressure profiles may also be generated for one or more of the alternative tracks using the pressure climatology for the selected cells of the grid. In some embodiments, at least one of the alternative pressure profiles for the historical tracks, the pressure profiles for the alternative tracks, and the alternative pressure profiles for the alternative tracks are modified based, at least in part, on the historical pressure profile along the historical track of the associated weather event.
In certain embodiments of the invention, the step of inputting data includes inputting data representative of a plurality of historical tracks and inputting data representative of atmospheric pressure associated with at least some of the plurality of points along the historical tracks. The atmospheric data defines historical pressure profiles of the historical tracks. In these embodiments, the step of generating data includes generating a plurality of alternative tracks for more than one of the historical tracks. Further, these embodiments include at least one of the following steps: a) generating one or more alternative pressure profiles for one or more of the historical tracks; b) generating one or more pressure profiles for one or more of the alternative tracks; and c) generating one or more alternative pressure profiles for one or more of the alternative tracks. These or other embodiments of the subject method may further comprise the step of extracting a subset of data from the data representative of the historical tracks, the alternative tracks, and the pressure profiles, based on climatological conditions for a selected time period.
Additional features and advantages will become apparent to those skilled in the art upon consideration of the following detailed description of illustrative embodiments exemplifying the best mode of carrying out the method as presently perceived.